I will present some recent results on single and double nanowires with proximity gap hosting Majorana and Para-fermions [1]. Typically, the topological phases are engineered by tuning the magnetic field to the topological threshold value of typically a few Teslas. However, the magnetic field has a detrimental effect on the host superconductor and so it is interesting to search for ways to achieve the topological phase without or with smaller B-fields. A particular way to achieve this goal is to exploit crossed Andreev pairing in a double nanowire setup [1,2,3] which destructively interferes with the direct pairing, and thereby lowers the threshold for the B-field substantially [3]. In re-examining the proximity effect in such finite-size geometries we discovered that the standard procedure of 'integrating out superconductivity' breaks down [2]. 

I will also present some recent results on hybrid platforms for quantum computing which combine spin qubits in quatum dots with topological qubits on a surface code architecture [4].

[1] J. Klinovaja and D. Loss, PRL 112, 246403 (2014); PRB 90, 045118 (2014). 

[2] C. Reeg, J. Klinovaja, and D. Loss, arXiv:1701.07107.

[3] C. Schrade, M. Thakurathi, C. Reeg, S. Hoffman, J. Klinovaja, and D. Loss, arXiv:1705.09364.

[4] S. Hoffman, C. Schrade, J. Klinovaja, and D. Loss. Phys. Rev. B 94, 045316 (2016).